The immunity–weight conjecture for Hurwitz orbits with simply intersecting cycles

Let $\Sigma$ be a homogeneous $B_3$-space covering a finite homogeneous $PSL(2,\mathbb{Z})$-space $\overline{\Sigma}$. Suppose that the cycles of $\overline{\Sigma}$ are simply intersecting. Immunity–weight conjecture. Then

$$\operatorname{imm}(\Sigma)\leq \omega(\Sigma).$$

This conjecture proposes that the immunity of a Hurwitz orbit is bounded by its weight under a weaker condition than the previously used bound on the lengths of $xy$-cycles. It concerns the cellular-automaton approach to estimating immunity in the classification of Nichols algebras; its resolution is not specified in the source.